Reset a column’s MultiIndex levels

Another solution is to use MultiIndex.droplevel with rename_axis (new in pandas 0.18.0):

import pandas as pd

cols = pd.MultiIndex.from_arrays([['basic_amt']*4,
                                     ['NSW','QLD','VIC','All']], 
                                     names = [None, 'Faculty'])
idx = pd.Index(['All', 'Full Time', 'Part Time'])

df = pd.DataFrame([(1,1,2,4),
                   (0,1,0,1),
                   (1,0,2,3)], index = idx, columns=cols)
                   
print (df)
          basic_amt            
Faculty         NSW QLD VIC All
All               1   1   2   4
Full Time         0   1   0   1
Part Time         1   0   2   3

df.columns = df.columns.droplevel(0)
#pandas 0.18.0 and higher
df = df.rename_axis(None, axis=1)
#pandas bellow 0.18.0
#df.columns.name = None

print (df)
           NSW  QLD  VIC  All
All          1    1    2    4
Full Time    0    1    0    1
Part Time    1    0    2    3

print (df.columns)
Index(['NSW', 'QLD', 'VIC', 'All'], dtype="object")

If you need both column names, use list comprehension:

df.columns = ['_'.join(col) for col in df.columns]
print (df)
           basic_amt_NSW  basic_amt_QLD  basic_amt_VIC  basic_amt_All
All                    1              1              2              4
Full Time              0              1              0              1
Part Time              1              0              2              3

print (df.columns)
Index(['basic_amt_NSW', 'basic_amt_QLD', 'basic_amt_VIC', 'basic_amt_All'], dtype="object")